The invention relates to a technique for adaptively removing a source of interference from a primary waveform that is masking a weaker waveform, and more particularly to a method for estimating the Doppler shift of interference moving through a field of separated sensors and adaptively cancelling the interference.
The broadband removal of unknown and time varying Doppler effects is motivated by the following problem. Consider a sparse field of distributed sensors S.sub.1 and S.sub.2 through which moves a strong source of interference, I, as illustrated in FIG. 1. Each sensor node S.sub.1 and S.sub.2 in the distributed field will sense the interference with a different Doppler shift due to the motion internal to the field. A target of interest is much weaker than the interference, and is detectable only by the node to which it is closest. Since the interference I is detected on both nodes S.sub.1 and S.sub.2 and the target T appears on only one node, a natural approach is to use other nodes as reference waveforms for the adaptive cancellation of the strong interference from the node detecting the weak target. The Doppler shifts tend to decorrelate the interferences, however, significantly degrading the performance of a conventional multiple LMS adaptive canceller.
The need, therefore, exists to adjust to the Doppler effects on spatially separated coherent components so that other nodes can be used to remove the interference energy that masks the weak signals of interest.
The conventional approach in adaptive cancellation is to use a reference measurement that is highly correlated with a component of a primary waveform that one wants to remove. That component can be strong jamming, for example, that masks a weak signal on the primary waveform The reference is usually input to the LMS adaptive filter, and the output is subtracted from the primary waveform. The resulting cancelled output, called the error waveform, is fed back to drive the adaptive filter to minimize the power in the error. The problem is that the Doppler shifts on the interference waveform between the reference and the primary decorrelate the broadband interference between the two. This severely degrades the ability of the canceller to suppress the interference. Thus, some method is needed to undo the Doppler effects, which are unfortunately unknown. The adaptive Doppler canceller of the present invention compensates for the Doppler effects and simultaneously estimates the Doppler parameter and cancels the interference.
It is known that digital Doppler "unstretching" can be used to induce (or to undo) a known Doppler shift on a broadband waveform. R. A. Mucci, "An Efficient Procedure for Broadband Doppler Compensation," Proceedings of the 1984 IEEE International Conference on Acoustics, Speech and Signal Processing," pages 47.9.-47.9.4.
Let s(t) denote the radiated signal. The medium is assumed to introduce attenuation and delay due to propagation over range R, additive noise, and no signal distortion. The received signal y(t) is then given by EQU y(t)=.alpha.(R)s(t-R/c)+n(t) (1)
where .alpha.(R) is the attenuation factor and c is the sound speed. If there is a relative velocity, V, between the radiator and the receiver, then EQU R=R.sub.o +Vt (2)
where R.sub.o is the range at time zero, and the received waveform is then EQU y(t)=e(R)s[1-a)t-]+n(t) (3)
where a=V/c and .tau.=R.sub.o /c.
The approach by Mucci. i.d., for removing Doppler effects is to interpolate and then decimate by different factors. The transmitted waveform is x(t), and the signal component of the received waveform is y(t)=x[(1-a)t]. The waveform is sampled at a high rate 1/T, i.e., at an interval of T seconds, so that the sampled waveform, denoted by y.sub.T (n) is given by EQU Y.sub.T (n)=y(nT)=x[(1-a)nT] (4)
The next step it to interpolate by an integer factor, L, forming an estimate of the radiated signal. EQU Y.sub.T/L (n).apprxeq.x[(1-a)nT/L] (5)
This is followed by decimation by an integer factor, K, producing a sequence of estimates of x(t) at uniformly spaced times spaced (1-a)KT/L. EQU Y.sub.TK/L (n).apprxeq.x[(1-a)KnT/L] (6)
Note that if K and L are chosen such that (1-a)K/L=1, then the sequence in eq. 6 provides estimates of the original waveform x(t) uniformly spaced T seconds apart in time, i.e., the Doppler shift is removed.
Mucci suggests the following implementation: 1) zero pad and low pass filter for the interpolation, and then 2) reduce the sample rate by K, i.e., take every K.sup.th sample Such an implementation does not take into account the effects of time varying, unknown Doppler shifts.